Manuscript Em01-D@2 · Em01-D-v2.tex · definition · d3b49151

Definition: Logarithmically homogeneous chain

The complete origin-germ certificate › Distributional dilation · lines 1291–1304

Em01-D@2#eq:chain

A chain $H_{0}, \dots, H_{J} \in D^{'} (R^{8})$ of degree $λ \in R$ satisfies

H_{j} (s \cdot) = s^{λ} k = 0 \sum^{j} \frac{( lo g s ) ^{k}}{k !} H_{j - k}, s > 0.

The chain is defined as distributions, including at the origin. A merely off-origin homogeneous expression is not enough.

Displayed formulas in this passage

Em01-D@2#eq:chain · line 1294
$H_{j} (s \cdot) = s^{λ} k = 0 \sum^{j} \frac{( lo g s ) ^{k}}{k !} H_{j - k}, s > 0.$